Interval Notation / Absolute Value Worksheet

Interval Notation / Absolute Value Worksheet

<p>Interval Notation / Absolute Value Worksheet Answers</p><p>Graph the given intervals and find their intersection.</p><p>1. ( -3, 2) and [ 1 , 4 ) intersection = [ 1 , 2 )</p><p>-3 1 2 4</p><p>2. ( - ∞, 3 ) and ( - 2 , + ∞ ) intersection = ( - 2 , 3 )</p><p>-2 3</p><p>Solve and graph each inequality.</p><p>3.  6x  2  5 7  6x  2  5  6  2  2  6x  7 Divided by a negative, inequality  6x 7  switches direction  6  6 7 x   6</p><p>7 4. 1  2x  3  4 x  1 , x  2 1  2x  3  4  3   3   3 2  2x  7 2 2x 7 1 7   2 2 2 2 7 1  x  2  1  5. x 1 x    0  2  TTTT FFFFFFFFF TTTT Critical points are … 1 1 1  x 1  0 and x   0 2 2 1 1 1  1    2 2 1 x  1 and x   2</p><p>TEST x = 0</p><p> 1  0 10    0  2   1  1   0  2  1   0 2</p><p>FALSE</p><p> 2  1  6. x x   x    0  3  3  Critical points are … 2 1 x  0 and x   0 and x   0 3 3 2 1 x  0, x  , x   3 3</p><p>TEST x = 1 TTTT FF TTT FFFF  2  1  11 1   0 1 2 3 3  0    3 3  1  4  1    0  3  3  4  0 FALSE 9 7. 4x3  6x 2  0 Critical points are … FFFF TTTT FFFF 2x 2 2x  3  0 0 3</p><p>2 2 2x  0 2x  3  0 3 x  0 x  2</p><p>TEST x = 1</p><p>413  612  0 4  6  0 TRUE  2  0</p><p>Solve the absolute value equations.</p><p>8. 6x  5  0</p><p>6x  5  0  5  5 6x  5 5 x   6</p><p>CHECK</p><p>  5  6  5  0  6   5  5  0 0  0 0  0 2 9. x 1  3 x 1  4  0 Let u = x 1</p><p> u 2  3u  4  0 u  4u 1  0</p><p> x 1  4  0 x 1  4</p><p>No solution, abs. value ≠ (-)</p><p> x 1 1  0 x 1  1</p><p>1  x 1  1 1  x 1  1 Solution set x = { 0 , - 2 } 1  1  1 - 2  x  0</p><p>CHECK</p><p>0 1 2  30 1  4  0 1 2  31  4  0 1 3  4  0 0  0</p><p> 2 1 2  3 2 1  4  0 1 2  31  4  0 1 3  4  0 0  0 Solve and find the solution for each absolute value inequality as an interval.</p><p>10. x  2  1</p><p>1  x  2  1  2   2  2 1 3 1  x  3 Interval ( 1 , 3 )</p><p>11. x  3  3</p><p> 3  x  3  3 - 6 0  3   3  3  6  x  0 Interval ( - ∞ , -6 ] U [ 0 , + ∞ )</p><p>12. 2x 1  1</p><p>1  2x 1  1 - 1 0 1  1  1  2  2x  0 Interval ( - ∞ , -1 ] U [ 0 , + ∞ )  2 2x 0   2 2 2 1  x  0</p><p>1 2 13.  2x   3 3 1 1  2 6 2 1 2   2x   3 3 3 1 1 1      3 3 3  1   1  Interval  ,    , 1 2 6   2x  1     3 1 1  x   6 2</p>

View Full Text

Details

  • File Type
    pdf
  • Upload Time
    -
  • Content Languages
    English
  • Upload User
    Anonymous/Not logged-in
  • File Pages
    5 Page
  • File Size
    -

Download

Channel Download Status
Express Download Enable

Copyright

We respect the copyrights and intellectual property rights of all users. All uploaded documents are either original works of the uploader or authorized works of the rightful owners.

  • Not to be reproduced or distributed without explicit permission.
  • Not used for commercial purposes outside of approved use cases.
  • Not used to infringe on the rights of the original creators.
  • If you believe any content infringes your copyright, please contact us immediately.

Support

For help with questions, suggestions, or problems, please contact us